BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Claremont Center for the Mathematical Sciences - ECPv6.15.17.1//NONSGML v1.0//EN CALSCALE:GREGORIAN METHOD:PUBLISH X-WR-CALNAME:Claremont Center for the Mathematical Sciences X-ORIGINAL-URL:https://colleges.claremont.edu/ccms X-WR-CALDESC:Events for Claremont Center for the Mathematical Sciences REFRESH-INTERVAL;VALUE=DURATION:PT1H X-Robots-Tag:noindex X-PUBLISHED-TTL:PT1H BEGIN:VTIMEZONE TZID:America/Los_Angeles BEGIN:DAYLIGHT TZOFFSETFROM:-0800 TZOFFSETTO:-0700 TZNAME:PDT DTSTART:20220313T100000 END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:-0700 TZOFFSETTO:-0800 TZNAME:PST DTSTART:20221106T090000 END:STANDARD BEGIN:DAYLIGHT TZOFFSETFROM:-0800 TZOFFSETTO:-0700 TZNAME:PDT DTSTART:20230312T100000 END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:-0700 TZOFFSETTO:-0800 TZNAME:PST DTSTART:20231105T090000 END:STANDARD BEGIN:DAYLIGHT TZOFFSETFROM:-0800 TZOFFSETTO:-0700 TZNAME:PDT DTSTART:20240310T100000 END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:-0700 TZOFFSETTO:-0800 TZNAME:PST DTSTART:20241103T090000 END:STANDARD BEGIN:DAYLIGHT TZOFFSETFROM:-0800 TZOFFSETTO:-0700 TZNAME:PDT DTSTART:20250309T100000 END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:-0700 TZOFFSETTO:-0800 TZNAME:PST DTSTART:20251102T090000 END:STANDARD BEGIN:DAYLIGHT TZOFFSETFROM:-0800 TZOFFSETTO:-0700 TZNAME:PDT DTSTART:20260308T100000 END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:-0700 TZOFFSETTO:-0800 TZNAME:PST DTSTART:20261101T090000 END:STANDARD END:VTIMEZONE BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20250407T161500 DTEND;TZID=America/Los_Angeles:20250407T171500 DTSTAMP:20260612T155153 CREATED:20250402T004832Z LAST-MODIFIED:20250402T004832Z UID:3749-1744042500-1744046100@colleges.claremont.edu SUMMARY:Applied Math Seminar: Ethan Epperly (Caltech) DESCRIPTION:Title: Randomly pivoted Cholesky: Fast\, accurate matrix approximation for scientific machine learning \nAbstract:\nLow-rank approximation of positive semidefinite matrices is a basic problem in computational mathematics\, with many applications to machine learning and scientific computing. Existing approaches for this problem largely fall into two categories: simple\, fast\, but sometimes inaccurate methods and sophisticated\, slower methods with accuracy guarantees. To achieve the best of both worlds\, this talk introduces randomly pivoted Cholesky\, an algorithm for positive semidefinite low-rank approximation that is simple\, fast\, and accurate. We demonstrate the effectiveness of randomly pivoted Cholesky for spectral clustering of molecular dynamics data\, achieving an order of magnitude lower clustering error than previous methods. We then go on to discuss theoretical guarantees for randomly pivoted Cholesky. Using a matrix concavity argument\, we show that randomly pivoted Cholesky has nearly optimal low-rank approximation properties. We conclude by discussing extensions and future prospects for this simple\, yet effective\, algorithm. URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-ethan-epperly-caltech/ LOCATION:Emmy Noether Room\, Estella 1021\, Pomona College\,\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20250324T161500 DTEND;TZID=America/Los_Angeles:20250324T171500 DTSTAMP:20260612T155153 CREATED:20250130T190206Z LAST-MODIFIED:20250311T055012Z UID:3672-1742832900-1742836500@colleges.claremont.edu SUMMARY:Applied Math Seminar: Ryan O'Dowd (Claremont Graduate University) DESCRIPTION:Title: Learning on manifolds without manifold learning \nAbstract: Function approximation based on data drawn randomly from an unknown distribution is an important problem in machine learning. The manifold hypothesis assumes that the data is sampled from an unknown submanifold of a high dimensional Euclidean space. A great deal of research deals with obtaining information about this manifold\, such as the eigendecomposition of the Laplace-Beltrami operator or coordinate charts\, and using this information for function approximation. This two-step approach implies some extra errors in the approximation stemming from estimating the basic quantities of the data manifold in addition to the errors inherent in function approximation. In this paper\, we project the unknown manifold as a submanifold of an ambient hypersphere and study the question of constructing a one-shot approximation using a specially designed sequence of localized spherical polynomial kernels on the hypersphere. Our approach does not require preprocessing of the data to obtain information about the manifold other than its dimension. We give optimal rates of approximation for relatively “rough” functions. URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-ryan-odowd-claremont-graduate-university/ LOCATION:Emmy Noether Room\, Estella 1021\, Pomona College\,\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20250310T161500 DTEND;TZID=America/Los_Angeles:20250310T171500 DTSTAMP:20260612T155153 CREATED:20250130T002924Z LAST-MODIFIED:20250303T200907Z UID:3668-1741623300-1741626900@colleges.claremont.edu SUMMARY:Applied Math Seminar: Sarah Robinson (Claremont McKenna College) DESCRIPTION:Title: Do Taxes Affect Pre-Tax Income Inequality? Evidence from 100 Years of U.S. States \nAbstract: We study how U.S. state taxes have affected pre-tax income inequality during the last century. Our primary analysis focuses on the top marginal personal income and corporate income tax\, and their effect on top incomes and top income shares within each state. The long panel nature of our data\, from 1917 to 2018\, allows us to study the effect of tax adoptions\, tax cancellations\, and tax changes\, and furthermore to assess both immediate and long-term relationships. With event study and synthetic control designs\, we generally find no statistically significant relationship between tax measures and inequality. Some of our point estimates\, as well as a simple two-way fixed effects analysis\, suggest that higher income taxes may reduce top incomes and income shares. URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-sarah-robinson-claremont-mckenna-college/ LOCATION:Emmy Noether Room\, Estella 1021\, Pomona College\,\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20250303T161500 DTEND;TZID=America/Los_Angeles:20250303T171500 DTSTAMP:20260612T155153 CREATED:20250130T002829Z LAST-MODIFIED:20250225T061553Z UID:3666-1741018500-1741022100@colleges.claremont.edu SUMMARY:Applied Math Seminar: Efstratios Tsoukanis (Claremont Graduate University) DESCRIPTION:Title: Bi-Lipschitz Invariants \nAbstract: Consider a finite-dimensional real vector space and a finite group acting unitarily on it. We investigate the general problem of constructing Euclidean stable embeddings of the quotient space of orbits. Our embedding relies on subsets of sorted coorbits with respect to chosen window vectors. Our main injectivity results examine the conditions under which such embeddings are injective. We establish these results using semialgebraic techniques. Furthermore\, our main stability result states and demonstrates that any embedding based on sorted coorbits is automatically bi-Lipschitz when injective. We establish this result using geometric function techniques. Our work has applications in data science\, where certain systems exhibit intrinsic invariance to group actions. For instance\, in graph deep learning\, graph-level regression and classification models must be invariant to node labeling. URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-efstratios-tsoukanis-claremont-graduate-university/ LOCATION:Emmy Noether Room\, Estella 1021\, Pomona College\,\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20250224T161500 DTEND;TZID=America/Los_Angeles:20250224T171500 DTSTAMP:20260612T155153 CREATED:20250214T080219Z LAST-MODIFIED:20250214T080318Z UID:3698-1740413700-1740417300@colleges.claremont.edu SUMMARY:Applied Math Seminar: Ryan Aschoff (UC Riverside) DESCRIPTION:Title: Smooth non-decaying solutions to the 2D dissipative quasi-geostrophic equations \nAbstract: In this talk we explore the two-dimensional dissipative surface quasi-geostrophic (SQG) equation with fractional diffusion of order 2α for α ∈ (1/2\,1]\, focusing on the setting where the initial data does not decay at spatial infinity and periodicity is not assumed. In geophysical applications\, the equations model shallow water currents with the scalar field θ is interpreted as the pressure\, while the associated velocity field u governs the fluid motion. Traditionally\, the transport velocity is recovered from the pressure via a constitutive law that fails when decay is absent. To overcome this\, we replace it with a generalized\, Serfati-type constitutive law—a method originally developed for the 2D Euler equations. \nWe will discuss how this approach enables us to prove the global existence and uniqueness of mild solutions\, as well as classical solutions (with data bounded in C^k\, for k≥2) without relying on spatial decay. The presentation will include an overview of the reformulated mild solution framework\, which couples the pressure and velocity equations via the fractional heat operator and a modified convolution structure. In addition\, we will outline extensions of this method to a Serfati-type SQG system and indicate how Littlewood-Paley techniques can be used to approach the inviscid case. URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-ryan-aschoff-uc-riverside/ LOCATION:Emmy Noether Room\, Estella 1021\, Pomona College\,\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20250217T161500 DTEND;TZID=America/Los_Angeles:20250217T171500 DTSTAMP:20260612T155153 CREATED:20250130T002710Z LAST-MODIFIED:20250210T172352Z UID:3665-1739808900-1739812500@colleges.claremont.edu SUMMARY:Applied Math Seminar: Denis Gaidashev (Uppsala University) DESCRIPTION:Title: Renormalization and wild attractors for Fibonacci maps \nAbstract: A Fibonacci map is a piecewise defined map of a subset of an interval I onto I with a unique critical point of order d whose orbit undergoes nearest returns at Fibonacci times. It has been shown by Bruin\, Keller\, Nowicki and van Strien that such maps exhibit “wild” attractors: Cantor sets of zero Lebesgue measure whose basin of attraction is meager but has positive Lebesgue measure. We will discuss real renormalization\, and a trichotomy for Fibonacci maps\, similar to the Avila-Lyubich trichotomy for Feigenbaum Julia sets\, which\, in particular\, allows us to show that Fibonacci maps admit wild attractors for d=5.1\, and do not for d=3.9 (and\, conjecturally\, for 21\, and we will show a new result concerning the existence of solutions for a boundary value problem with this operator. URL:https://colleges.claremont.edu/ccms/event/emer-lopera-arias-hmc/ LOCATION:Emmy Noether Room\, Estella 1021\, Pomona College\,\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Ami Radunskaya":MAILTO:aradunskaya@pomona.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20240422T161500 DTEND;TZID=America/Los_Angeles:20240422T173000 DTSTAMP:20260612T155153 CREATED:20240421T181538Z LAST-MODIFIED:20240421T181538Z UID:3442-1713802500-1713807000@colleges.claremont.edu SUMMARY:İrma Hacınlıyan (Istanbul Technical University) DESCRIPTION:Title: On Nonlinear Schrödinger Type Equations: Wave Modulation and Mathematical Analysis \nAbstract: The nonlinear Schrödinger (NLS) equation describes the evolution of slowly varying packets of quasi-monochromatic waves in weakly nonlinear dispersive media. The NLS equation with soliton solutions is one of the significant and widely pursued research areas on the nonlinear wave motions. Sub-studies on such evolution equations include derivations of those equations; finding exact solutions and developing methods for these; studies of the analytic and geometric structure of the equations as integrable systems; singularities and collapses of solutions; analyzing modulation equations by dynamical systems methods; and related subjects. In this talk\, nonlinear modulation of waves propagating in a generalized elastic solid according to different physical scenarios will be discussed. Properties of the solutions of NLS-type equations that are derived using the reductive perturbation method will be examined by mathematical analysis methods. URL:https://colleges.claremont.edu/ccms/event/irma-hacinliyan-istanbul-technical-university/ LOCATION:Emmy Noether Room\, Estella 1021\, Pomona College\,\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Ami Radunskaya":MAILTO:aradunskaya@pomona.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20240401T161500 DTEND;TZID=America/Los_Angeles:20240401T171500 DTSTAMP:20260612T155153 CREATED:20240330T172834Z LAST-MODIFIED:20240330T172834Z UID:3426-1711988100-1711991700@colleges.claremont.edu SUMMARY:Chiu-Yen Kao (Claremont McKenna College) DESCRIPTION:Title: Geometric Optimization Involving Partial Differential Equations and Its Applications \nSpeaker: Professor Chiu-Yen Kao\, Claremont McKenna College\, Claremont\, CA USA \nAbstract: Optimal geometric design for energy functionals\, which depends on solutions to partial differential equations\, provides a vast number of interesting and challenging mathematical problems. One of the famous problems is that L. Rayleigh conjectured that the disk should minimize the fundamental frequency of vibration (the square root of the first Laplace-Dirichlet eigenvalue) among all shapes of equal area\, more than a century ago. In this talk\, we will share our recent findings related to geometric optimization for eigenvalue problems. Our approach involves the development of various computational methods to optimize Steklov eigenvalues and Laplace-Beltrami eigenvalues. Additionally\, we explore applications of these methods. URL:https://colleges.claremont.edu/ccms/event/chiu-yen-kao-claremont-mckenna-college/ LOCATION:Emmy Noether Room\, Estella 1021\, Pomona College\,\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Ami Radunskaya":MAILTO:aradunskaya@pomona.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20240325T161500 DTEND;TZID=America/Los_Angeles:20240325T171500 DTSTAMP:20260612T155153 CREATED:20240330T173049Z LAST-MODIFIED:20240330T173059Z UID:3427-1711383300-1711386900@colleges.claremont.edu SUMMARY:Ami Radunskaya (Pomona College) DESCRIPTION:Title:  Can a function tell us how immune cells kill? \nSpeaker: Prof. Ami Radunskaya (Pomona College\, Claremont CA) \nAbstract: The immune system is able to fight cancer by mustering and training an army of effector “killer” cells.  Mathematical models of tumor-immune interactions must describe the proliferation\, recruiting and killing rates of immune cells.  Earlier work surprisingly showed that the functions describing the kill rates distinguish between two types of immune cells.  The mechanisms behind these differences have been a mystery\, however.  In an attempt to unravel this mystery\, we have created a cell-based fixed-lattice model that simulates immune cell and tumor cell interaction involving tumor recognition and two killing mechanisms.  These mechanisms play a big role in the effectiveness of many cancer immunotherapies. Results from model simulations\, along with theories developed by ecologists\, can help to illuminate which mechanisms are at work in different conditions. URL:https://colleges.claremont.edu/ccms/event/ami-radunskaya-pomona-collegeo/ LOCATION:Emmy Noether Room\, Estella 1021\, Pomona College\,\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Ami Radunskaya":MAILTO:aradunskaya@pomona.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20240318T161500 DTEND;TZID=America/Los_Angeles:20240318T171500 DTSTAMP:20260612T155153 CREATED:20240313T230255Z LAST-MODIFIED:20240330T174651Z UID:3405-1710778500-1710782100@colleges.claremont.edu SUMMARY:Sigifredo Herron (UNAL) DESCRIPTION: URL:https://colleges.claremont.edu/ccms/event/fernando-a-gallego-unal/ LOCATION:This event is virtual. Zoom link: https://pomonacollege.zoom.us/my/radzoom\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Ami Radunskaya":MAILTO:aradunskaya@pomona.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20240304T161500 DTEND;TZID=America/Los_Angeles:20240304T171500 DTSTAMP:20260612T155153 CREATED:20240228T002704Z LAST-MODIFIED:20240228T002704Z UID:3399-1709568900-1709572500@colleges.claremont.edu SUMMARY:Gabe Chandler (Pomona College) DESCRIPTION:Title: Graphical Anomaly Detection for High Dimensional and Object Data \nAbstract: Anomaly detection is an important task in data analysis\, though an agreed upon definition of what constitutes an outlier does not exist.  Accordingly\, a graphical tool that can highlight interesting observations in a data set that the scientist can then investigate with domain specific knowledge would be of value.  The depth quantile function (DQF)\, a recently introduced feature map that takes data of arbitrary dimension to a function of a single variable while encoding certain geometric information\, will provide such a tool.  After introducing the DQF\, we will discuss adaptations that make it particularly suited to the problem of anomaly detection\, particularly the case where the non-anomalous data is living on a lower dimensional manifold in the data space.  The DQF is also kernelizable\, allowing applications to non-Euclidean data\, as will be demonstrated via several examples. URL:https://colleges.claremont.edu/ccms/event/gabe-chandler-pomona-college/ LOCATION:Emmy Noether Room\, Estella 1021\, Pomona College\,\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Ami Radunskaya":MAILTO:aradunskaya@pomona.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20240226T161500 DTEND;TZID=America/Los_Angeles:20240226T171500 DTSTAMP:20260612T155153 CREATED:20240220T215244Z LAST-MODIFIED:20240220T224116Z UID:3391-1708964100-1708967700@colleges.claremont.edu SUMMARY:Javier Gonzalez Anaya (Harvey Mudd College) DESCRIPTION:This is the continuation of the semester’s joint seminar with the Universidad Nacional de Colombia-Manizales. \nTitle: Enumerating linearity regions of max-pooling layers in convolutional neural networks \nAbstract: Convolutional neural networks (CNN’s) are central tools in the application of machine learning to text\, audio and image processing. Their success stems from the ability of these networks to identify key features in complex datasets at a relatively low computational cost. Max-pooling layers (MPL’s) are key components of CNN’s that reduce the number of parameters used by the network while making it more robust to small changes in the input data. From a mathematical point of view\, MPLs are piecewise-linear functions\, and their number of linearity regions can be interpreted as a measure of complexity of the layer. In this talk I will explain how we can use combinatorial techniques to count these linearity regions\, and survey our current results in the area. URL:https://colleges.claremont.edu/ccms/event/javier-gonzalez-anaya-harvey-mudd-college/ LOCATION:Emmy Noether Room\, Estella 1021\, Pomona College\,\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Ami Radunskaya":MAILTO:aradunskaya@pomona.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20240219T161500 DTEND;TZID=America/Los_Angeles:20240219T171500 DTSTAMP:20260612T155153 CREATED:20240220T215909Z LAST-MODIFIED:20240220T215909Z UID:3392-1708359300-1708362900@colleges.claremont.edu SUMMARY:Cristian Lopez Morales (UNAL) DESCRIPTION:Join us for the first talk in the joint seminar with CCMS Applied Math and the Universidad Nacional de Colombia \nTitle \nSerre Conjecture. Geometric interpretation of the Quillen-Suslin Theorem. \nAbstract: \nThe Quillen-Suslin theorem asserts that over the polynomial ring with coefficients in a field K[x_1\,…\,x_n]\, every projective module is free. Despite the algebraic nature of the objects involved in this theorem and its proof\, this is a problem motivated by geometry. \n\nOriginally\, this problem was proposed by the French mathematician Jean-Pierre Serre as one of his famous conjectures. In this talk\, we will discuss the original formulation of Serre’s conjecture (the Quillen-Suslin theorem)\, along with the necessary concepts to translate the geometric statement into the algebraic one. URL:https://colleges.claremont.edu/ccms/event/cristian-lopez-morales-unal/ LOCATION:Emmy Noether Room\, Estella 1021\, Pomona College\,\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Ami Radunskaya":MAILTO:aradunskaya@pomona.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20240212T161500 DTEND;TZID=America/Los_Angeles:20240212T171500 DTSTAMP:20260612T155153 CREATED:20240207T150322Z LAST-MODIFIED:20240207T150322Z UID:3378-1707754500-1707758100@colleges.claremont.edu SUMMARY:Dagan Karp (Harvey Mudd College) DESCRIPTION:Title: Tropical Linear Series\n\nAbstract: In this talk I’ll attempt to give a friendly and example-driven introduction to the theory of linear series on tropical curves. While in some respects mirroring the classical study of linear series\, in the tropical setting there are many surprises and even basic questions remain open. This work is joint with Chang Chih-Wei\, Hernan Iriarte\, David Jensen\, Sam Payne\, and Jidong Wang. URL:https://colleges.claremont.edu/ccms/event/dagan-karp-harvey-mudd-college/ LOCATION:Estella 1021 (Emmy Noether Room)\, Pomona College\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Ami Radunskaya":MAILTO:aradunskaya@pomona.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20240129T041500 DTEND;TZID=America/Los_Angeles:20240129T171500 DTSTAMP:20260612T155153 CREATED:20240125T032110Z LAST-MODIFIED:20240125T032138Z UID:3350-1706501700-1706548500@colleges.claremont.edu SUMMARY:Applied Math Seminar: Adolfo Rumbos (Pomona College) DESCRIPTION:Title: Existence and multiplicity of solutions for a cooperative elliptic system using Morse theory \nThis is joint work with Leandro Recova (Cal Poly Pomona) \nAbstract URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-adolfo-rumbos-pomona-collegeo/ LOCATION:Emmy Noether Room\, Estella 1021\, Pomona College\,\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Ami Radunskaya":MAILTO:aradunskaya@pomona.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20231113T041500 DTEND;TZID=America/Los_Angeles:20231113T171500 DTSTAMP:20260612T155153 CREATED:20230912T154722Z LAST-MODIFIED:20231110T160645Z UID:3205-1699848900-1699895700@colleges.claremont.edu SUMMARY:Applied Math Seminar: Adam Yassine (Pomona College) DESCRIPTION:Title: On the Composition of Classical Mechanical Systems \nAbstract: Compositionality is a basic principle for understanding the physical world. The underlying idea is to study a system by studying the ways in which the components of the system compose to form the system. Category theory is an area in mathematics that is particularly well-suited for studying questions about compositionality. This talk will outline a way to use category theory to study classical mechanical systems from a compositional perspective. URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-adam-yassine-pomona-college/ LOCATION:Estella 1021 (Emmy Noether Room)\, Pomona College\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Ami Radunskaya":MAILTO:aradunskaya@pomona.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20231106T161500 DTEND;TZID=America/Los_Angeles:20231106T171500 DTSTAMP:20260612T155153 CREATED:20230912T155411Z LAST-MODIFIED:20230912T155411Z UID:3206-1699287300-1699290900@colleges.claremont.edu SUMMARY:Applied Math Seminar: Claremont Colleges Course Previews for Spring 2024 DESCRIPTION:During this student-centered Applied Math Seminar\, there will be discussion and presentations about upcoming courses offered in applied mathematics\, to help students make their enrollment choices for Spring 2024 and beyond. URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-claremont-colleges-course-previews-for-spring-2024/ LOCATION:Estella 1021 (Emmy Noether Room)\, Pomona College\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Ami Radunskaya":MAILTO:aradunskaya@pomona.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20231030T161500 DTEND;TZID=America/Los_Angeles:20231030T173000 DTSTAMP:20260612T155153 CREATED:20231019T153510Z LAST-MODIFIED:20231023T034142Z UID:3292-1698682500-1698687000@colleges.claremont.edu SUMMARY:Applied Math Seminar: Jeremy Brandman (DCS corporation) DESCRIPTION:Title \nControl algorithms for unmanned underwater vehicles: new approaches based on Hamilton-Jacobi equations and reinforcement learning. \nAbstract \nUnmanned underwater vehicles (UUVs) are defined by their ability to operate without direct human intervention.  As a result\, UUVs are valuable for surveillance tasks\, especially in the presence of hazardous environmental conditions. Specific applications of UUVs include seafloor mapping\, mine detection\, and oil pipeline inspection. \nIn this talk\, we propose new algorithms for two aspects of UUV control: path planning and vehicle guidance.  Path planning identifies a vehicle trajectory\, based on anticipated environmental conditions\, that achieves desired mission objectives (e.g. obstacle avoidance\, minimization of energy consumption). Vehicle guidance responds to observed environmental conditions in order to maintain fidelity to the path selected by the path planner. \nThe first half of this talk considers a new approach to path planning based on solving Hamilton-Jacobi partial differential equations (PDE).  The starting point for this method is the observation that the vehicle’s minimum travel-time satisfies a time-independent Hamilton-Jacobi equation .  Numerical solutions to this PDE are efficiently computed using the fast sweeping method.  Our approach is validated through several examples for which optimal trajectories are derived using the calculus of variations. \nThe second half of this talk introduces a reinforcement learning framework for incorporating in situ ocean current measurements into the guidance system in an energetically optimal manner.  Scaling and symmetry considerations turn out to play an important role in the framework’s efficiency and robustness.  Numerical results demonstrate that the energetic cost of transits executed under the guidance of a trained agent approaches optimal performance. URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-jeremy-brandman/ LOCATION:Estella 1021 (Emmy Noether Room)\, Pomona College\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Ami Radunskaya":MAILTO:aradunskaya@pomona.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20231023T161500 DTEND;TZID=America/Los_Angeles:20231023T171500 DTSTAMP:20260612T155153 CREATED:20230912T154613Z LAST-MODIFIED:20231023T033921Z UID:3203-1698077700-1698081300@colleges.claremont.edu SUMMARY:Applied Math Seminar: Evan Rosenman (CMC) DESCRIPTION:Title:  Recalibration of Predicted Probabilities Using the “Logit Shift”: Why Does It Work\, and When Can It Be Expected to Work Well? \nAbstract: In the context of election analysis\, researchers frequently face the “recalibration problem.” That is: they must reconcile individual-level vote probabilities\, modeled prior to the election\, with vote totals observed in each precinct once the election has taken place. Making these adjustments such that the probabilities match known aggregates\, researchers can obtain better-calibrated estimates of key quantities such as vote preferences among subgroups of the electorate defined by race\, age\, and gender. \nWe provide theoretical grounding for one of the most commonly used recalibration strategies\, known colloquially as the “logit shift.” The logit shift is a heuristic adjustment\, in which a constant correction on the logit scale is found\, such that aggregated predictions match observed totals. \nWe show that the logit shift offers a fast and accurate approximation to a principled\, but computationally impractical adjustment strategy: computing the posterior probabilities\, conditional on the observed totals. After deriving analytical bounds on the quality of the approximation\, we illustrate its accuracy using Monte Carlo simulations. We also discuss scenarios in which the logit shift is less effective at recalibrating predictions: when the totals are available only for highly heterogeneous populations\, and when the original predictions correctly capture the mean of true individual probabilities\, but fail to capture the shape of their distribution. URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-evan-rosenman-cmc/ LOCATION:Estella 1021 (Emmy Noether Room)\, Pomona College\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Ami Radunskaya":MAILTO:aradunskaya@pomona.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20231009T161500 DTEND;TZID=America/Los_Angeles:20231009T171500 DTSTAMP:20260612T155153 CREATED:20230912T154505Z LAST-MODIFIED:20231004T015412Z UID:3202-1696868100-1696871700@colleges.claremont.edu SUMMARY:Applied Math Seminar: Dan Pirjol (Stevens Institute of Technology) DESCRIPTION:Title: The Hartman-Watson distribution: numerical evaluation and applications in mathematical finance \nAbstract: The Hartman-Watson distribution appears in several problems of applied probability and financial mathematics. Most notably\, it determines the joint distribution of the time-integral of a geometric Brownian motion and its terminal value. A classical result by Yor (1981) expresses it as a one-dimensional integral which is however difficult to evaluate numerically in the region of interest for financial applications. The talk gives an introduction to the HW distribution and presents an asymptotic expansion which can be used for an efficient numerical evaluation. Two applications from mathematical finance are discussed: Asian options pricing in the Black-Scholes model\, and option pricing in the log-normal SABR model. URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-dan-pirjol-stevens-institute-of-technology/ LOCATION:Estella 1021 (Emmy Noether Room)\, Pomona College\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Ami Radunskaya":MAILTO:aradunskaya@pomona.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20231002T161500 DTEND;TZID=America/Los_Angeles:20231002T171500 DTSTAMP:20260612T155153 CREATED:20230912T154332Z LAST-MODIFIED:20230929T050112Z UID:3201-1696263300-1696266900@colleges.claremont.edu SUMMARY:Applied Math Seminar: Tin Thien Phan (Los Alamos National Laboratory) DESCRIPTION:Title: Understanding SARS-CoV-2 viral rebounds with and without treatments. \nAbstract: In most instances\, the characteristics of SARS-CoV-2 mirror the patterns of an acute infection\, with viral load rapidly peaking around 5 days post-infection and subsequently clearing within 2 weeks. However\, some individuals show signs of viral recrudescence of up to 10000 viral RNA copies/mL shortly following viral remission. These instances of viral resurgence\, distinct from long COVID\, are generally resolved within four weeks post-infection and have been observed across varying treatment statuses\, vaccination statuses\, and viral strains. In this presentation\, I will review existing evidence of transient viral rebound and demonstrate that a class of dynamic models that incorporates virus-immune interaction accurately describes transient viral rebound dynamics under different treatment scenarios\, including those untreated. While these models all share a simple structure with a unique globally-asymptomatic-stable disease-free equilibrium\, the most exciting and relevant aspect hides within their transient phase and remains largely unexplored. URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-tin-thien-phan-los-alamos-national-laboratory/ LOCATION:Estella 1021 (Emmy Noether Room)\, Pomona College\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Ami Radunskaya":MAILTO:aradunskaya@pomona.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20230918T161500 DTEND;TZID=America/Los_Angeles:20230918T171500 DTSTAMP:20260612T155153 CREATED:20230912T153609Z LAST-MODIFIED:20230912T162421Z UID:3198-1695053700-1695057300@colleges.claremont.edu SUMMARY:Applied Math Seminar: Michael Murray (UCLA) DESCRIPTION:Title: Towards Understanding the Success of First Order Methods in Training Mildly Overparameterized Networks \nAbstract: For most problems of interest the loss landscape of a neural network is non-convex and contains a plethora of spurious critical points. Despite this first order methods such as SGD and Adam are in practice remarkably successful at finding optimal\, or at the least near optimal\, minimizers of the loss. In recent years the Neural Tangent Kernel has proven a powerful tool in explaining this phenomena and for providing guarantees for highly overparameterized networks. However\, for mildly overparameterized networks (where width scales linearithmically in the sample size) where richer feature learning can occur an explanation is lacking. In this talk I will present recent results on the loss landscape of two-layer mildly overparameterized ReLU networks. Our approach involves bounding the dimension of the sets of local and global minima using the rank of the Jacobian of the parameterization map. Using results on random binary matrices\, we show most activation patterns correspond to parameter regions with no bad differentiable local minima. Furthermore\, for one-dimensional input data\, we show most activation regions realizable by the network contain a high dimensional set of global minima and no bad local minima. We experimentally confirm these results by finding a phase transition from most regions having full rank to many regions having deficient rank depending on the amount of overparameterization. URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-michael-murray-ucla/ LOCATION:Estella 1021 (Emmy Noether Room)\, Pomona College\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Ami Radunskaya":MAILTO:aradunskaya@pomona.edu END:VEVENT END:VCALENDAR